We left our X-Men in 1962, after they intervened in the Cuban missile crisis. Fast forward to "the future" and 1973, and you have the setting(s) for the most recent X-Men installment, Days of Future Past. In the future, mutants have come under attack by Sentinels (robots built to annihilate mutants). A small group of surviving X-Men sends Wolverine back to 1973, when Mystique killed the mastermind behind the Sentinels (which only sped up their production and added to their mutant-killing efficiency, as Mystique was caught and her DNA was extracted for scientific use).
Wolverine's mission (and the bulk of the movie's action) is convincing Mystique not to go through with the assassination, in the hopes that the Sentinel program won't progress. There are, of course, several other things to take care of for that to happen and what seems like a straightforward plan gets a few snags along the way. Professor X--Charles Xavier--is holed up in his defunct institute while he staves off paralysis with the help of a serum that also dulls his telepathic powers. Magneto is imprisoned below the Pentagon. Mystique is as headstrong and unwilling to listen to logic as ever. Wolverine has his work cut out for him.
Luckily, as the viewer, all you have to do is sit back and watch him/them work. Which I suggest doing, preferably with some popcorn.